While the received literature on unionized duopolies emphasized the key role of inter-union competition in reversing the standard Cournot-Bertrand profit ranking, in this paper such issue is studied in a framework with labour decreasing returns and a centralized (industry-wide) union, hence in a context where inter-union competition is clearly absent. Nevertheless, it is shown that the "reversal result" can apply provided that union is sufficiently wage oriented. Furthermore, it is pointed out that, in the special case of total wage bill maximization, it applies for a larger range of the degree of product substitutability under a central union rather than under firm-specific unions.